Two high-speed automated packaging lines, Line A and Line B, are used to process identical orders. The time taken by Line A to process an order, in seconds, is normally distributed with mean 12.5 and variance 0.36. The time taken by Line B to process an order, in seconds, is normally distributed with mean 13.2 and variance 0.64. Processing times for all orders and lines are independent.
Determine the probability that, for a single randomly selected order, Line B completes the packaging faster than Line A.
A factory uses these lines to process a batch of 150 orders on Line A and a separate batch of 150 orders on Line B. Both lines start simultaneously.
Calculate the probability that the total time taken by Line B to complete its batch exceeds the total time taken by Line A by more than 120 seconds.
390 exam-style questions on OCR (MEI) A Level Maths 2.4 Probability Distributions, covering 2.4.1 Recognise binomial situations, 2.4.2 Probability of success p, 2.4.3 Calculate binomial probabilities, 2.4.4 Mean of the binomial distribution, 2.4.5 Expected frequencies for binomial, 2.4.6 Probability functions and discrete random variables, 2.4.7 Numerical probabilities for a simple distribution, 2.4.8 Normal distribution as a model (A-level only), 2.4.9 Shape of the Normal curve (A-level only), 2.4.10 Linear transformation and standardising (A-level only), 2.4.11 Symmetry and inflection of Normal curve (A-level only), 2.4.12 Calculate probabilities from a Normal distribution (A-level only), 2.4.13 Model with probability distributions, and 2.4 Probability Distributions. Each one has a worked solution and a mark scheme showing where the marks go.